t^2+t=84

Solution for t^2+t=84 equation:

t^2+t=84

We move all terms to the left:

t^2+t-(84)=0

a = 1; b = 1; c = -84;
Δ = b2-4ac
Δ = 12-4·1·(-84)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{337}}{2*1}=\frac{-1-\sqrt{337}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{337}}{2*1}=\frac{-1+\sqrt{337}}{2}
$